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Okay, so say you play an instant or sorcery spell and then play Increasing Vengeance targeting it could you then play Swerve changing the target of Increasing Vengeance from the random instant or sorcery to itself?

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If by "itself" you mean having Increasing Vengeance target itself, then no, you can't do that because rule 114.4 says

A spell or ability on the stack is an illegal target for itself.

Even if you could do that, it wouldn't do much because no matter how many times an Increasing Vengeance were to resolve copying itself, you would still end up with a single Increasing Vengeance.

If, on the other hand, you mean having Increasing Vengeance target Swerve, then you can do that but it wouldn't do much because once Increasing Vengeance starts to resolve Swerve would no longer be on the stack so the Increasing Vengeance would be countered for having no legal target.

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murgatroid's answer is correct that you can't have Increasing Vengeance target itself. But even if you had two copies of Increasing Vengeance that could target one another, you still wouldn't have an infinite combo. Infinite loops can only consist of mandatory actions - unless someone does something different, the loop will repeat by itself over and over without anyone having to make any decision other than passing priority. That is not the case here, because each copy of Increasing Vengeance requires a selection for the target. You can shortcut the loop as many times as you like, but you can't say that you'll repeat an optional loop indefinitely - you pick how many times you want to do it, and then you are required to take a different action. You cannot force a draw by entering a loop that has optional actions which are required to keep it going.

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    Colloquially, an "infinite loop" or "infinite combo" in Magic refers to any sequence of actions that can be repeated in a loop an unbounded number of times, not just mandatory loops. Your objection here is unfounded. – murgatroid99 Jun 23 '20 at 19:32
  • In addition, it is in fact possible to construct a mandatory loop as you describe. If the original spell is countered in response to the second Increasing Vengeance, the Increasing Vengeance copy has no legal target other than the first Increasing Vengeance. – murgatroid99 Jun 23 '20 at 19:32
  • @murgatroid99 Fair enough, but in the absence of anything else pertinent in the question, seemingly the only useful thing this loop could accomplish is forcing a draw, which it would not under most circumstances. Agree I'm kind of splitting hairs with the "infinite loop" terminology, but I think it's worth pointing out the difference between "infinite" loops that must be terminated after a finite number of cycles, and truly infinite loops that do not terminate and result in a draw. – Nuclear Hoagie Jun 23 '20 at 19:53
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    But the distinction you're making doesn't match how that term is actually used. – murgatroid99 Jun 23 '20 at 20:30
  • And there are cards like Ral, storm conduit which gain a benefit from this type of loop. – Eggi Jun 24 '20 at 6:22

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